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Grothendieck's beautiful theory of schemes permeates modern algebraic geometry and underlies its applications to number theory, physics, and applied mathematics. This simple account of that theory emphasizes and explains the universal geometric concepts behind the definitions. In the book, concepts are illustrated with fundamental examples, and explicit calculations show how the constructions of scheme theory are carried out in practice.
List of contents
Basic Definitions.- Examples.- Projective Schemes.- Classical Constructions.- Local Constructions.- Schemes and Functors.
About the author
The author taught at Brandeis University for twenty-seven years, with sabbatical time spent in Paris, Bonn, and Berkeley, and became Director of the Mathematical Sciences Research Institute in Berkeley in the Summer of 1997. At the same time he joined the faculty of UC Berkeley as Professor of Mathematics. In 2003 he became President of the American Mathematical Society. He currently serves on several editorial boards (Annals of Mathematics, Bulletin du Société Mathématique de France, Springer-Verlag's book series Algorithms and Computation in Mathematics).
Summary
Grothendieck's beautiful theory of schemes permeates modern algebraic geometry and underlies its applications to number theory, physics, and applied mathematics. In the book, concepts are illustrated with fundamental examples, and explicit calculations show how the constructions of scheme theory are carried out in practice.
Report
"A great subject and expert authors!"
Nieuw Archief voor Wiskunde,June 2001
"Both Eisenbud and Harris are experienced and compelling educators of modern mathematics. This book is strongly recommended to anyone who would like to know what schemes are all about."
Newsletter of the New Zealand Mathematical Society, No. 82, August 2001
